Semi-Lagrangian Finite-Element Exterior Calculus for Incompressible Flows

2023/01/12 by Tonnon, Wouter, Hiptmair, Ralf · 2 citations
#65D99 (Secondary) #65M60 (Primary) #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2301.04923

Abstract

We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully discrete version of the scheme enjoys excellent stability properties in the vanishing viscosity limit and is applicable to inviscid incompressible Euler flows. Conservation of energy and helicity are enforced separately.

Cited by

• Structure-preserving Variational Multiscale Stabilization of the Incompressible Navier-Stokes Equations
• H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions

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